Heat oil in large pot over medium heat. Add onion and garlic and cook until soft, 6 to 8 minutes. Add broth and bring to a simmer. Add kale, broccoli, and peas. Cook until vegetables are just tender, about 8 minutes. Puree in batches with immersion blender or in standing blender until smooth. Season with kosher salt and black pepper to taste. Serve topped with eggs and prosciutto.

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